Efficient vectorised Cuda kernels for high-order finite element flow solvers

In this work, we develop efficient kernels for elemental operators of matrix-free solvers of the Helmholtz equation, which are the core operations for more complete Navier-Stokes solvers. We consider straight-sided and deformed quadrilateral elements from unstructured high-order meshes. We investigate two types of efficient CUDA kernels for a range of polynomial orders; a first type which maps each elemental operation to a CUDA-thread, and a second that maps each element to a CUDA-block. Our results show that the first option is beneficial for small elements with low polynomial order, whereas the second option is beneficial for larger elements. For both options we show the importance of the right layout of data structures, and analyse the effect of utilising different memory spaces on the GPU

An isoparametric approach to high-order curvilinear boundary-layer meshing

This is the final version of the article. Available from Elsevier via the DOI in this record.The generation of high-order curvilinear meshes for complex three-dimensional geometries is presently a challenging topic, particularly for meshes used in simulations at high Reynolds numbers where a thin boundary layer exists near walls and elements are highly stretched in the direction normal to flow. In this paper, we present a conceptually simple but very effective and modular method to address this issue. We propose an isoparametric approach, whereby a mesh containing a valid coarse discretization comprising of high-order triangular prisms near walls is refined to obtain a finer prismatic or tetrahedral boundary-layer mesh. The validity of the prismatic mesh provides a suitable mapping that allows one to obtain very fine mesh resolutions across the thickness of the boundary layer. We describe the method in detail for a high-order approximation using modal basis functions, discuss the requirements for the splitting method to produce valid prismatic and tetrahedral meshes and provide a sufficient criterion of validity in both cases. By considering two complex aeronautical configurations, we demonstrate how highly stretched meshes with sufficient resolution within the laminar sublayer can be generated to enable the simulation of flows with Reynolds numbers of 106 and above.This work was partly supported by EU Grant No. 265780 as part of the EU FP7 project “IDIHOM: Industrialization of High-Order Methods — A Top-Down Approach”. We would like to thank Dr. Tobias Leicht of DLR for asking a very pertinent question concerning the validity of the generated high-order mesh that we believe to have answered in this article. We also thank Jean-Eloi Lombard for his assistance in generating the mesh for Fig. 15

Automatic generation of 3D unstructured high-order curvilinear meshes

This is the final version of the article. Available from the publisher via the DOI in this record.The generation of suitable, good quality high-order meshes is a significant obstacle in the academic and industrial uptake of high-order CFD methods. These methods have a number of favourable characteristics such as low dispersion and dissipation and higher levels of numerical accuracy than their low-order counterparts, however the methods are highly susceptible to inaccuracies caused by low quality meshes. These meshes require significant curvature to accuratly describe the geometric surfaces, which presents a number of difficult challenges in their generation. As yet, research into the field has produced a number of interesting technologies that go some way towards achieving this goal, but are yet to provide a complete system that can systematically produce curved high-order meshes for arbitrary geometries for CFD analysis. This paper presents our efforts in that direction and introduces an open-source high-order mesh generator, NekMesh, which has been created to bring high-order meshing technologies into one coherent pipeline which aims to produce 3D high-order curvilinear meshes from CAD geometries in a robust and systematic way

Alkaline earth complexes of a sterically demanding guanidinate ligand

The synthesis of the guanidine MesN{C(NCy2)}N(H)Mes (LH; Mes = 2,4,6-Me3C6H2, Cy = cyclohexyl), and its use as a proligand for the synthesis of alkaline earth metal complexes are reported. Described herein are (i) an unusual Hauser base cubane, (ii) a homoleptic and a base-stabilized magnesium complex featuring the same guanidinate ligands, and (iii) the comparison of a series of alkaline earth (Mg, Ca, Sr, Ba) bis(guanidinate) complexes, which allows the opportunity to compare the changing trends in bonding as the Group is descended. The reaction between LH and MeMgI(OEt2)2 yields the Hauser base as a mixture of the tetramer [Mg4L4(μ3-I)4] (1a) and dimer [Mg2L2(μ-I)2(OEt2)2] (1b), and the reaction with two equivalents of MgnBu2 leads to the formation of four-coordinate [MgL2] (2), which features a square-planar geometry for the magnesium cation, or five-coordinate [MgL2(THF)] (3), depending on the solvent used. 1a is the first crystallographically-characterized cubane structure to consist of four LAeX (L = ligand, X = halide) units. The complexes [AeL2(THF)2] (Ae = Ca, 4; Ae = Sr, 5) and [BaL2] (6) were synthesized via redox transmetallation/ligand exchange reactions. Complex 6 is the first example of a homoleptic, monomeric barium complex of the NCN ligand family, with the structure stabilized by a number of barium-arene interactions in the solid state

A Thermo-elastic Analogy for High-order Curvilinear Meshing with Control of Mesh Validity and Quality

This is the final version of the article. Available from Elsevier via the DOI in this record.In recent years, techniques for the generation of high-order curvilinear mesh have frequently adopted mesh deformation procedures to project the curvature of the surface onto the mesh, thereby introducing curvature into the interior of the domain and lessening the occurrence of self-intersecting elements. In this article, we propose an extension of this approach whereby thermal stress terms are incorporated into the state equation to provide control on the validity and quality of the mesh, thereby adding an extra degree of robustness which is lacking in current approaches